System for measuring ultrasonically the elastic properties of a moving paper web

ABSTRACT

The invention relates to a system for measuring ultrasonically the elastic properties of a moving paper web. A noise type ultrasonic sound wave is generated by an ultrasonic sound generating device in the web at an excitation point. A reference ultrasonic wave reradiated into the air from the excitation point is indicated. A pick-up device is provided for receiving ultrasonic sound reradiated from the paper web at a predetermined distance form the location of the sound generating device. The ultrasonic sound generating device and the reference ultrasonic receiving device are provided on the same side of the paper web. At least one of these two kinds of devices includes a number of elements provided symmetrically in relation to the other device.

This invention concerns the measurement of the velocity of ultrasound,in-plane, for a moving paper web. The ultrasound velocity in paper isknown to be related to various measures of paper strength and stiffness.

BACKGROUND OF THE INVENTION

The most important values for the papermaker to consider from ultrasoundvelocity measurements on paper web are:

TSO Tensile Stiffness orientation, i.e. the orientation of the elasticproperties in-plane of the paper sheet,

TSI_(MD) Tensile Stiffness Index in the machine direction of the papermachine,

TSI_(CD) Tensile Stiffness Index in the cross direction of the papermachine.

It is possible to determine these quantities and also the anisotropyratio TSI_(MD) /TSI_(CD) by performing the ultrasound velocitymeasurements in the machine direction (MD), cross direction (CD) anddirections between (MD) and (CD). The tensile stiffness and anisotropyratio characterize the paper quality.

The velocity of an ultrasonic pulse propagating in-plane of a papersheet corresponds with the sheet's elastic properties, i.e. the TSI. TSIcan be compared to Young's modulus (or "Emodulus") for other materials.The relationship can be expressed by:

    TSI=v.sup.2 * c

where TSI is measured in kNm/g, v is the propagation velocity (km/sek)for the ultrasonic pulse, and c is a dimensionless constant close to 1depending on Poisson's ratio for the paper. The velocity is easilydetermined by measuring the propagation time for an ultrasonic pulsebetween a transmitter and a receiver.

These quantities are often measured statically on samples taken from apaper web. However, it is desirable to measure these paper qualitieson-line by an on-line meter used as a sensor for the continuous controlof a paper manufacturing process.

Most of the known on-line meter arrangements (U.S. Pat. No. 4,291,577,U.S. Pat. No. 4,688,423, U.S. Pat. No. 4,730,492) employ rotatingwheels, which contain transmitters and receivers of ultrasonic waves.These wheels are rotated by a moving paper web, that requires a directphysical contact between the wheels and the web. The ultrasound velocityis usually determined from the delay time of an ultrasonic signalbetween the particular transmitter and receiver.

In order to obtain a reasonable measurement accuracy the wheels must bysynchronized which makes the system extremely complicated andunreliable. An arrangement described in U.S. Pat. No. 4,688,423overcomes this drawback by employing disk type transducers which can beexcited continuously and, therefore, synchronization of the wheels isnot necessary. However, the arrangements described in theabove-mentioned patent specifications need a direct mechanical contactbetween the ultrasonic transducers and the web.

In a papermaking machine the fast moving web vibrates in the directionnormal to the web surface, creating a randomly changing force applied tothe wheels. The amplitude of excited and received ultrasonic wavesdepends on the pressure between particular ultrasonic transducer and theweb. Due to the randomly changing force, the amplitudes of receivedsignals fluctuate, thereby making the results of measurements lessaccurate.

The physical contact with the web is not needed if ultrasonic waves areexcited and detected optically, as described in U.S. Pat. No. 5,025,665.Ultrasonic waves in the paper web are generated by means of a laser.This wave is detected at a determined distance from the excitation pointby means of another laser beam, reflected from the web. The velocity ofthe ultrasonic wave is obtained from the measured delay time between theexcitation instant and the time of the wave arrival.

The disadvantage of this optical system is that the amplitudes of theultrasonic waves propagating in-plane of the web are very small. A verystrong acoustic noise exists in papermaking machines, which isaccompanied by the vibrations of the moving web. In fact this makes theoptical detection of the lowest order symmetrical Lamb waves impossible,and only these waves are suitable for measurements of the stiffness andtensile strength of paper.

A method and device for continuously determining the modulus ofelasticity of advancing flexible material, such as paper web, in acontactless fashion is disclosed in WO91/17435. An ultrasonic wave trainis transmitted through the air towards the web. The ultrasonic wavesscattered through the air by the material are sensed at a distance d,about tventy to fourty centemeters from the transmission point at thesame side of the web, no reference ultrasonic wave receiving means beingprovided for receiving a reference ultrasonic wave from the transmissionpoint.

Other prior on-line paper measuring systems are disclosed in theU.S.S.R. Pat. No. 489018 and U.S.S.R. Pat. No. 489036, and described inthe publication by Kazys (the inventor of the present invention),Proceedings of 20th international conference on Acoustics, Praque, 1981,p.p. 6-10. The ultrasound velocity in a moving paper web was determinedby exciting broad band noise-like ultrasonic wave by means of dryfriction, receiving the ultrasonic wave reradiated by the web by twonon-contacting ultrasonic receivers and calculating thecross-correlation function between these two received signals.

The first receiver was placed opposite to the ultrasonic transmitter andthe second at a determined Distance from the transmitter along the web.

In order to improve the signal/noise ratio, a rotating cylinder wasplaced underneath the web close to the second ultrasonic receiver. Thedelay time was determined from the delay of the peak value of thecross-correlation function. The advantage of this measuring systemcompared to the ones described above was that it had no moving orrotating parts involved in the active measuring facilities.

The disadvantages of the measuring system described in theabove-mentioned USSR-patents are that the excitation and reception ofthe ultrasonic waves are performed from the opposite sides of the web.Also, the signal/noise ratio is not sufficient high enough to permitreliable continous on-line measurements in a mill environment. Anotherproblem which is encountered in performing measurements in otherdirections than the web propagation direction is an even worsesignal/noise ratio due to the higher losses of ultrasonic waves in ananisotropic material.

The main object of the present invention is to provide an on-linemeasuring system with single side access to the paper web, performingmeasurements at different directions in-plane of a moving web.

Another object of the present invention is to provide an on-linemeasuring system having improved in noise robustness for the system in apaper mill environment.

Still another object is to provide an on-line dust-insensitive measuringsystem.

Yet another object is to provide an on-line measuring system providingwell-defined and precise measuring results.

These objects are achieved with a system having the characterizingfeatures disclosed in the main claim. Further features and furtherdevelopments of the invention are disclosed in the subclaims.

SUMMARY OF THE INVENTION

The present invention solves the problems associated with the prior artand other problems by providing a system for continuous measurements ofthe velocity of ultrasonic waves in a moving paper web. The foregoing isaccomplished by exciting a broad-band noise type Lamb wave in the web byhaving the source of ultrasonic waves and all the ultrasonic receiversplaced on a single side of the web. The broad band noise-like Lamb wavein the paper web is generated by means of dry friction between themoving web and the friction head. The system has no moving parts and allsignals are received by non-contacting means.

The delay time of the ultrasonic wave is preferably determined as a zerocross of the Hilbert transform of the cross-correlation function of thereceived signals, corresponding to the maximum value of thecross-correlation function.

In order to make the system noise robust, i.e. provide a lowsignal/noise ratio, the receiving of the reradiated ultrasonic waves isperformed above the rotating cylinder of a paper making machine at theparticular position in respect to the line, where the moving web touchesthe cylinder for the first time. The pick-up is preferably made by twomicrophones having such a distance from each other that airborneultrasound waves from the friction head are reduced and ultrasound wavespropagating through the paper web are enhanced.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and forfurther objects and advantages thereof, reference is now made to thefollowing description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 illustrates schematically a measuring system according to theprior art,

FIG. 2 illustrates schematically a first embodiment of a measuringsystem according to the invention,

FIG. 3A and 3B illustrates different friction head/microphonecombinations,

FIGS. 4A, 4B and 5A, 5B and 6A, 6B illustrate different embodiments offriction head and microphone units,

FIG. 7A illustrates schematically a side view of a second embodiment ofa measuring system according to the invention,

FIGS. 7B and 7C illustrate a schematic view from above of twoembodiments of the system i FIG. 7A having the possibility of measuringthe ultrasound velocity in different directions,

FIG. 7D illustrates a graph to provide an extrapolated value of theultrasound velocity in the cross direction,

FIGS. 8A to 8D are diagrams of signals provided in different operationsteps in searching for the delay time of the ultrasonic wave transmittedthrough the paper web, and

FIG. 9 is a flow chart of the processing operation in order to providethe delay time of the ultrasonic wave in-plane of the paper web,

The same references are used for the same elements in the Figures.

With reference to FIG. 1, a prior art on-line paper measuring systemdisclosed in the U.S.S.R. Pat. No. 489018 includes a friction head 1provided on one side of a moving paper web 2 generating a noise-likeultrasonic signal v_(w) as a result of dry friction between the head 1and the web 2. A random signal with a normal law of distribution up to70 to 90 kHz is excited. The part of this signal v_(w) propagating inthe paper web 2 as the zero order symmetrical Lamb wave s₀ is theinteresting one to examine. The excited wave is reradiated partiallyinto the surrounding air and is picked up by a contactless referencemicrophone Mic1 provided opposite the head 1 on the other side of theweb 2, and by a contactless pick-up microphone Mic2 provided on the sameside of the web as the reference microphone Mic1 but a determineddistance 1₀ away from, i.e. downstream from, the head 1 along the web inits moving direction, below called "the machine direction". In order tohave an enhanced reradiation of the propagated wave from the web to theair the web 2 is supported by a rotating cylinder 3 opposite the pick-upmicrophone Mic2. The signals from the microphones Mic1 and Mic2 are fedto a processing unit 4', which correlates the two signals in order toderive the propagation time through the web, so that the velocity of theultrasonic wave in the paper web can be computed and the resultspresented on a display 5'.

From a commercial point of view, a measuring system in which all unitsare located at the same side of a paper web has many advantages.However, in order to implement one side access approach it is necessaryto overcome a lot of problems.

1. According to prior art, the reference microphone could not be put atthe same distance from a signal source as the pick-up microphone is froma paper web, because both the reference microphone and the signal sourcehad to be located on the same side of the web. For the same reason thereference microphone surface usually could not be perpendicular to apropagation direction of the signal in air, and that caused asignificant reduction in a normalized cross-correlation (covariance)function value or a distortion of its shape.

2. The location of the signal source unit and both the referencemicrophone and the pick-up microphone for the waves propagated along theweb on the same side creates a direct wave propagating in air that ismuch stronger than in the case of a two-side access, because then thepaper web is not shielding the airborne ultrasonic wave. It reduces adegree of correlation between the transmitted and received signals too.

3. The friction head causes an abrasion of the paper and scrapes offfibres which produces dust. If it is placed on the same side of the webas the microphones this dust will be transported to the microphones,which will reduce noticeably their sensitivity and distort theirfrequency response, if the same kind of friction heads are used as inprior art.

Therefore, a new kind of friction head 4 adapted to a referencemicrophone M1 is provided according to the invention illustratedschematically in the embodiments of the invention shown in FIGS. 2 and6.

The main feature of the combination of the friction head 4 and thereference microphone M1 is that friction and microphone elements areprovided symmetrically to each other. This means that there could be onefriction element and an even number of microphone elements providedsymmetrically in relation to the friction element such that themicrophones in each pair have the same distance to the friction element,or there could be one microphone element and an even number of frictionelements placed around the microphone element. The friction elementshave preferably a nearly pointlike contact with the paper web.

FIG. 3A shows a first embodiment of the friction head/referencemicrophone combination in which one element A of the first kind isprovided between two elements B1, B2 of the other kind. FIG. 3B showsanother embodiment in which one element A' of the first kind issurrounded by four elements C1, C2 and D1, D2 of the other kind, eachpair C1, C2 and D1, D2 being placed diagonally in relation to the firstkind of element A'. From a practical point of view the element A or A'is preferably a microphone element, since then it is not necessary tobalance the signals from several elements. However, friction elementswill cause dust in the environment and measures must be taken tominimize the influence of dust on the microphone(s). Thus, the preferedembodiment, shown in FIG. 3A, is to have a microphone between twopointlike friction elements placed along a line perpendicular to themachine direction, i.e. the moving direction of the paper web. If morethan two friction elements are provided they must all be provided at theside of a line through an ultrasonic sound receiving element of thereference means directed in the machine direction of the moving paperweb in order to prevent dust from coming directly onto the microphone.

Three embodiments of the unit of the friction head and referencemicrophone having the preferred configuration mentioned above are shownin FIGS. 4A, 4B and 5A, 5B and 6A, 6B, respectively. The FIGS. 4A, 5A,and 6A show the actual appearance of the units when a noise shield isprovided in order to minimize air borne sound waves from reaching themicrophone, and the FIGS. 4B, 5B, and 6B show the units without thenoise shield.

Two friction parts, 6, 7 in FIG. 4B, 8, 9 in FIG 5B, and 10, 11 in FIG.6B, are placed such that their contact point with the paper web isprovided on each side of the ultrasonic reference microphone 13, 14 or15, respectively, along a line perpendicular to the machine direction ofthe web. The friction parts are preferably made from a hard alloymaterial, for instance tungsten carbide. The friction parts are held bya holder 16, 17 or 18, respectively.

The distance D between the friction parts is much less than thewavelength of the ultrasonic wave in the web. Also, the dimensions ofthe contact area between the friction parts and the paper web are lessthan the wavelength of the ultrasonic wave in the web. Thus, this kindof friction source acts substantially like a two-point-source. Thedistance between the contact areas and the plane of the referencemicrophone is comparable with the wavelength in air for the generatedultrasonic waves (for f₀ =40 kHz, λ_(a) /2=4.3 mm, where f₀ is thecenter frequency of the signal spectrum, and λ_(a) is the wavelength ofthe center frequency in air).

The signals provided in the web by the friction parts are captured bythe reference microphone M1 provided as close as possible to the middlepoint between the friction parts. In order to reduce the waves radiatednot by the contact area by the friction parts and transmitted throughthe air to the reference microphone M1 the noise shield 19, 20 and 21,respectively, is placed around the friction parts and held by theirholder and is provided with an opening adapted to hold the referencemicrophone in place. The noise shield also protects the microphone fromat least some of the dust caused by the friction between the parts andthe web, and this effect is enhanced if the noise shield has its sidesturned towards the microphone somewhat nearer to the web than its outersides thus directing the dust outwardly.

Each of the two parts 6, 7 of the friction head in FIGS. 4A and 4B has atriangular form having its base angled to the paper web. This frictionhead provides the best measuring result but it scratches the paper. Eachof the two parts 8, 9 of the friction head in FIGS. 5A and 5B are formedas hemispheres, which has a substantially lesser affect on the paper webthan the head in FIGS. 4A, 4B; however, the measuring result issatisfying but not as good as from the head 6, 7. The friction parts 8,9 are made of hard alloy and comprise tips, contacting the web, coveredby a material absorbing ultrasonic waves, for example, a soft rubber.Each of the two friction parts 11, 12 of the friction head in FIGS. 6Aand 6B are formed as rounded pins angled to the web and could be seen asa compromise between the other two embodiments of the friction head asregards scratching the paper web and providing well distinguishablesignals through the web.

Returning to FIG. 2, the signal part of the ultrasonic wave v_(w)transmitted through the web of interest to be indicated is the s₀ wavesignal, which corresponds to the symmetric zero order Lamb wavespropagated in the web 2, i.e. the fastest propagating wave. The so wavereradiated from the web is captured by a pick-up microphone M2 locatedopposite to the contact line C1 between the rotating cylinder and theweb 2 from which the best reradiation into the air of the s₀ wavepropagated in the web is provided.

The lateral dimension of the pick-up microphone M2, and also of thereference microphone M1, are at least 10 times less than a wavelength ofthe ultrasonic wave in the paper web, and the microphones are placed ata distance from the web less than a wavelength of the ultrasonic wave s₀reradiated by the web into air.

Noise is also radiated into the air from the contact line C₂ where theweb 2 first meets the cylinder 3. This noise should preferably besuppressed as far as possible and therefore a noise suppressing shield25, for example made of rubber, is provided around the microphone M2shielding it from the noise from the contact line C₂ and also fromambient noise. Thus, its outer edge nearest to the contact line C₂ islocated downstream of this line. The shield has a small inner diameterso that the microphone M2 is placed close to its internal edge.

In order to make an extra shield for the microphone M2 both regardingthe airborne noise from the friction head and against the dust from it anumber of shields 26 are provided above the paper web between themicrophone M1 and the rotating cylinder 3.

The signal from the reference microphone M1 is fed to a first input of aprocessor 27 through an amplifier 28 and a bandpass filter 29. Thesignal from the pick-up microphone M2 is fed to a second input of theprocessor 27 through an amplifier 30 and a bandpass filter 31. Theprocessor 27 will make a cross-correlation operation on the signals fromthe two microphones. Preferably this operation will include a Hilberttransform. An example of this kind of operation will be given below inconnection with the embodiment shown in FIG. 7. The example given therefor the somewhat more complicated embodiment could easily be amended tobe adapted to the embodiment in FIG. 2 by a person skilled in the art.

In accordance with the invention measures are taken to enhance thesignal/noise ratio of the correlated signals, particularly in a noisyenvironment. Therefore, in accordance with a second embodiment of theinvention, shown in FIG. 7A, a double channel measuring receivingmicrophone device is provided to receive the wave propagated along theweb 2. It is, however, to be noted that more than two pick-upmicrophones can be provided according to the invention.

In the second embodiment of the invention at least two pick-upultrasonic microphones Mic2A and Mic2B, being the pick-up elements ofthe pick-up receivers, are placed a distance 1_(m) from each other, thedistance being chosen to be a half-wavelength of the wave in air at thecentre frequency of the bandwidth of the ultrasonic wave transmittedthrough the web. The microphone Mic2A is located opposite the contactline C₁. The microphone Mic2B is located on the side of the microphoneMic2A turned away from the friction head 4.

Thus the principle of the operation is based on a difference ofultrasound velocities in air (v_(a) =343 m/sek) and paper (v_(s0) 1.5 to4 km/sek). The signals at the outputs of the microphones Mic2A and Mic2Bare given by:

    u.sub.2a (t)=y.sub.s (t)+y.sub.a (t)+n.sub.md (t)n.sub.0a (t)

    u.sub.2b (t)=k.sub.s *y.sub.s (t-Δt.sub.s)+k.sub.a *y.sub.a (t-Δt.sub.a)+k.sub.n *n.sub.md (t+Δt.sub.a)+n.sub.0b (t)

where u_(2a) (t) and u_(2b) (t) are the complete wave signal at theoutput of the microphones Mic2A and Mic2B, respectively, y_(s) (t) isthe s₀ wave signal at the output of the microphone Mic2A, y_(a) is theairborne wave generated by the friction head, n_(md) is the noisepropagating along the machine direction at the output of the microphone,n_(0a) (t) and n_(0b) (t) are electronic noise and ambient noisepropagating along directions others than the machine direction, k_(s),k_(a), and k_(n) are the coefficients reflecting the asymmetry of themicrophones Mic2A and Mic2B for the appropriate waves, Δt_(s) =l_(m)/v_(s0) is the delay time of the s₀ wave between the microphones, andΔt_(a) =l_(m) /v_(a) is the delay time of airborne waves between themicrophones propagating along the machine direction.

Due to extensive differences in the ultrasonic velocities in the web andin air, Δt_(s) <<Δt_(a), Δt_(s) <t₀, t₀ =1/f₀, where f₀ is the centerfrequency of the signal spectrum. Therefore, the spectral componentswith frequencies equal or close to frequency f₀ are approximately:##EQU1##

Then, addition of the signals from the two microphones Mic2A and Mic2Bgives the following result:

    u.sub.2 (t)=u.sub.2a (t)+u.sub.2b (t)=(1+k.sub.s)*y.sub.s (t)+(1-k.sub.a)*y.sub.a (t)+(1-k.sub.n)*n.sub.md (t)+n.sub.0a (t)+n.sub.0b (t)

The coefficients k_(s), k_(a), k_(n) are close to 1, which givesapproximately:

    u.sub.2 (t)=2*y.sub.s (t)+ε.sub.a y.sub.a (t)+ε.sub.n n.sub.md (t)+ n.sub.0a (t)+n.sub.0b (t)!

where ε_(a) and ε_(n) are much lower than 1, which indicates that theamplitude of the s₀ wave signal is amplified twice and the amplitudes ofthe wave propagating in air along the machine direction from thefriction head is substantially reduced, like the noise propagating inthe machine direction. The electronic noises or the noises arriving fromdirections different from the machine direction are not suppressed andare added as partially correlated or uncorrelated random processes.

It is to be noted that the distance l_(m) between the pick-upmicrophones could be chosen in another way, but then the equations aboveand the combination of them will be changed. The main feature of thechoise of distance is that the term y_(s) (t) is essentially enhancedand the term y_(a) (t) essentially reduced in the combination.

Also, as in the embodiment shown in FIG. 2, a noise reducing shield 35,for instance of rubber, is placed around the microphones Mic2A and Mic2Bin order to reduce the noise from the noisy surroundings. The shield 35,having the same function as the shield 25 in the embodiment shown inFIG. 2, has preferably, the shape of its lower side adapted to the shapeof the paper web when it is transferred over the rotating cylinder 3,and has its wall placed quite close to the microphones Mic2A and Mic2B.

Referring now to the embodiment having the pick-up microphones placedone half-wavelength of the airborne ultrasonic wave apart, in order toestimate the velocity of the s₀ wave a cross-correlation should be madeon the signals from the reference microphone M1 and the added signalsfrom the two pick-up microphones Mic2A and Mic2B. The signals from thepick-up microphones are amplified in respective amplifiers 36 and 37 andthen added in an adder 38. The signal from the adder 38 is fed to thesecond input of the processor 27 through a bandpass filter 39.

The processor 27 is provided with a program for performing an automatictime delay measurement in order to obtain the velocity of the wave inthe actual paper web.

The delay time is determined from the cross-correlation function. Forthis purpose two methods are combined, namely, cross-correlationfunction envelope peak detection for a coarse evaluation andzero-crossing detection of the cross-correlation function Hilberttransform for the accurate measurements. Time diagrams illustrating thistechnique are given in FIGS. 8A to 8D. This techique is efficient in thecase of relatively narrow-band signals, i.e., when a cross-correlationfunction has an oscillating character.

Therefore, as shown in FIG. 8A a cross-correlation function R_(XY) (τ)between transmitted and received s₀ wave signal at the outputs of thereceivers M1, 28, 29, and Mic2A, Mic2B, 36, 37, 38, 39 is provided

    R.sub.xy (τ)=(1/T)∫ x(t)+n.sub.1 (t)!* 2y.sub.a (t+τ)+ε y.sub.a (t+τ)+n.sub.md (t+τ)!+n.sub.2 (t+τ)!dtO

where T is the signal duration used for calculation, x(t) and y(t+τ) arethe signals from input channel M1, 28, 29, and the output channel Mic2A,Mic2B, 36, 37, 38, 39, respectively, and n₁ (t) is the noise received bythe microphone M1 and n₂ (t+τ) is the added noise received by themicropones Mic2A and Mic2B.

A zero-cross of the Hilbert transform of the cross-correlationcorresponding to the maximum value of the cross-correlated function ismade.

Then, the envelope, as shown in FIG. 8B, of a cross-correlation functionRxy(τ) is obtained by means of the Hilbert transform:

    A.sub.xy (τ)=√ R.sup.2.sub.xy (τ)+R.sup.2.sub.xy (τ)!

(see FIG. 8C), where ##EQU2## is the Hilbert transform of across-correlation function R_(xy) (τ) and shown in FIG. 8D. FIG. 8Cshows the detection of the envelope peak shown in FIG. 8B.

In the presence of signals propagating through multiple paths, thecross-correlation function has a few peaks, corresponding to differentdelays. Then the envelope function can be presented as ##EQU3## whereτ_(d1), τ_(d2) . . . are the delays in the corresponding paths.Therefore, in a general case not just one but a few peaks will bedetected. The proper peak is found by taking into account priorknowledge of the expected time of arrival, and usually is that closestto the zero instant.

The obtained rough estimate of the delay time τ_(d).sbsb.i is used toproduce a window H(t) in a time domain the width of which Δτ is slightlyless than half a period of oscillation of the band-limitedcross-correlation function

    Δτ<t.sub.0 /2

The window is located symmetrically in respect to the determined delaytime τ_(d).sbsb.i ##EQU4## The accurate delay time estimation isobtained from the windowed Hilbert transform R_(w) (t) of the initialcross-correlation function:

    R.sub.w (t)=H(t-τ.sub.d.sbsb.i)*R.sub.xy (t)

The peak value of the envelope function A_(xy) (τ) corresponds to thepeak value of the cross-correlation function R_(xy) (τ) only in the caseof non-dispersive propagation. As it was noted above, the symmetrical s₀wave used for the measurements propagates without noticeable dispersion.On the other hand, the uncertainty in detecting the rough delay timeshould be less than t₀ /2.

For a 35 kHz center frequency, rough delay time uncertainties of as muchas t₀ /2=14 μs can be allowed. Usually this requirement is easilyfullfilled and no ambiguity occurs.

The peak values of the cross-correlation function Rxy(τ) correspond tothe zero values of the Hilbert transform R_(xy) (τ). Hence, the time ofsignal arrival now can be found using simple zero-crossing technique(FIG. 8D):

    R.sub.w (t).sub.t =τ.sub.d1 =H(t-τ.sub.d.sbsb.i)*R.sub.xy (τ)=τ.sub.d1 =0

It is worthwhile to remember, that by shifting the window function H(t)to the locations of other envelope peaks τ_(d).sbsb.i, the accuratedelay times of signals propagating through different paths may beautomatically determined.

A flowchart of a program in the processor 27 for automatically derivingthe time delay is shown in FIG. 9 and includes shifting of the windowΔτ, shown in FIG. 8D, in several steps in order to find the searchedtime delay τ_(d) for the paper web 2.

The algorithm consists of three main stages: cross-correlation envelopefunction fitting by 2nd order polynomial; finding the peaks; and findingtheir classification according to a sharpness.

The algorithm starts from the window generation in the time domain. Thewidth of the window is given in terms of sampling points and defines thenumber of points used in the analysis. The window is shifted step bystep in subsequent algorithm loops. The size of this step defines theseparation between two neighbouring peaks and can be chosen in such away that minor peaks caused by a random noise or spurious waves would beignored.

The cross-correlation envelope function fitting is needed for findingthe peak and is performed by the least-square method using the 2nd orderpolynomial. Such a polynomial can have a positive or negative curvaturedepending on what kind of local extremity--a peak or a minimum has beenfound.

Strictly speaking, the 2nd order polynomial fitting always finds a localminimum or maximum independently of how they were created--by delayedsignals or by random noise fluctuations. The influence of localfluctuations can be reduced by increasing the width of the window. Thenthe peaks caused by delayed waves are usually sharper than the other,spurious, peaks.

Therefore, the peak finding procedure consists of the first orderderivative calculation, which enables the determination of the locationsof all extremities and the 2nd order derivative calculation, whichallows sorting them into maximums and minimums and, consequently,selection of the proper peak (or peaks) according to its (or their)sharpness. The sharpness ε is given by τdi the magnitude of the 2ndderivative of the peak.

The delay time estimate τ_(di) obtained from this peak is used togenerate the window H(t) mentioned above.

The Hilbert transform of the cross-correlation function .sup. R_(xy) (t)is multiplied by the windowing function H(t). All these functions arediscrete in the time domain. The spacing between two adjacent points isequal to the sampling period Δt_(s). In order to obtain measurementerrors less than the signal sampling interval Δt_(s), the segment of theHilbert transform is fitted using the least-square method by the 5thorder polynomial. Then the Equation has five roots, but only the rootinside the created window is selected. This root is a fine time delayt_(di) estimation. The wave velocity v₀ =l₀ /t_(di), and the tensilestiffness TSI=c₁ *v₀ ², where c₁ is a dimensionless constant close to 1depending on Poisson's ratio for the paper. The flowchart in FIG. 8 isbelieved to be self-explanatory and is therefore not described infurther detail.

It is necessary to point out that if the peak of the cross-correlationfunction caused by the s₀ -Lamb wave is the biggest, then the envelopefunction fitting can be omitted and the rough estimate of the peak delayobtained directly from the measured cross-correlation or envelopefunction. The other steps in the algorithm remain the same.

The method above has been described for measurement of the time delay inthe machine direction and this will give the tensile stiffness indexTSI_(MD) in the machine direction of the paper machine. The frictionhead 4, the microphones M1, Mic2A and Mic2B are then located in linewith the machine direction. However, as mentioned in the introductorypart of the specification the tensile stiffness index TSI_(CD) in thecross direction of the paper machine, and in directions between TSI_(MD)and TSI_(CD), are also needed in order to calculate the anisotropy ratioand the tensile stiffness orientation. An embodiment for also providingthese quantities will now be described with reference to FIGS. 7B and7C, even though the same feature naturally can also be provided for theembodiment shown in FIG. 2.

As is apparent from FIG. 7B, several sets of microphones Mic3A, Mic3B;Mic4A, Mic4B etc are shown located parallel to each other and oblique tothe microphone M1 in relation to the machine direction (the respectiveangular directions α_(N-1), α_(N) etc), such that each microphone Mic3A,Mic4A is situated tangentially in the same location above the rotatingcylinder 3 as the microphone Mic2A. The delay time of the symmetricalLamb wave propagating in that oblique direction, α_(N-1), α_(N) etc, ismeasured in the same way as described above for the ultrasonic Lamb wavepropagation in the machine direction, account being taken of thesomewhat longer propagation path for each set.

Instead of providing an array of receiving pick-up microphone sets onlyone set need be provided, said set being movable along the cylinderabove the web so as to be put in different oblique positions, i.e.scanning along the line C1. In this case, it is important to place theset of microphones, accurately in precise positions above the web (samedistance to the web and along line C1) in order to have the samemeasuring conditions for each measured oblique setting (not shown in aseparate figure, however the pick-up microphone set will be placed inthe same way as shown in FIG. 7B).

Another embodiment shown in FIG. 7C, has only one pick-up microphone setMic2A', Mic2B' and moves, as a unit, friction head 4 and referencemicrophone M1 across the web, for instance along a straight line F1parallel to the line C1, as shown, and derives the delay time for the s₀wave for a chosen amount of settings of the unit 4,M1 having differentangular positions in relation to the pick-up microphone set. It is alsopossible to move the friction-head/microphone set 4, M1 along a curvedline F2 (dashed), or to provide the velocity measurement along themachine direction separately and the measurements in the obliquedirections along a line F3 (dot/dashed) perpendicular to the line C1.

It should be noted that, even for the embodiments having scanningelements along a line and one element constantly in the same position,each measuring result is provided having both kinds of elements in thesame position in relation to each other during the time it takes to getthe measuring result.

Many different kinds of numerical methods may be used to provide a quiteprecise guess about the s₀ wave rate in the cross direction of the paperweb. One method is to fit the measured so wave rates for the differentoblique positions in some kind of periodic function, e.g. the functionfor an ellipse or some kind of Fourier serie.

Example in which a trigonometric first order Fourier series is used:

We assume that the ultrasonic velocity of the s₀ wave has been measuredin three different directions and these three different values are usedfor determining constants a0, a1 and b1. The constants are then insertedin the following formula:

    f(α)=a0+a1*cos2α+b1*sin2α                (1)

The estimated velocity is also dependent on formula 2:

    f(x)=k1*x+k2 (where x=f(α)max/f(α)min)         (2)

The constants k1 and k2 are known. A combination of the functions 1 and2 will give the following function which determines the so wave velocityin the cross direction (α=90°).

    v(CD)=f(x)*(a0-a1)                                         (3)

By changing the constants k1 and k2 it is possible to get the velocityin any direction from the formula 4:

    v(α,max/min)=(k1(α)*x+k2(α))*(a0+a1*cos2α+b1*sin2.alpha.)                                                     (4)

Another advantageous way to derive the velocity of the s₀ wave in thecross direction from the results from the different settings of thefriction-head/reference-microphone and the pick-up microphones inrelation to each other is to set the measuring results of the so waverates in a coordinate system, with the rate in the machine directionalong the X-axis and the rate in the cross direction of the web alongthe Y-axis, in relation to the respective angular deviation α_(N-1),α_(N) etc of each set to the machine direction in the way shown in FIG.7D. A curve is drawn through the different measuring results andextrapolated to cut the Y-axis in order to provide the velocity of theso wave in the web in the cross direction. A small extrapolation erroris unavoidable but is minimized by having a lot of settings of thefriction-head/reference-microphone in relation to the pick-upmicrophones--the more, the better.

The same extrapolation technique as shown in FIG. 7D can be used alsofor the embodiments shown in FIG. 7C.

While the invention has been described with reference to specificembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention asapparent from the Claims. In addition, modifications may be made withoutdeparting from the essential teachings of the invention. For instance,more than two pick-up microphones could be provided at the rotatingcylinder.

We claim:
 1. A system for measuring ultrasonically the elasticproperties of a moving paper web, comprising:a. means for generating anoise type ultrasonic sound wave in the web at an excitation point; b.reference ultrasonic wave receiving means for receiving contactlessly areference ultrasonic wave reradiated into the air from the excitationpoint; c. pick-up ultrasonic wave receiving means for receivingultrasonic wave reradiated from the paper web a predetermined distancefrom the location of the ultrasonic wave generating means for use indetermining the elastic properties of the moving paper web, wherein theultrasonic sound generating means and the reference ultrasonic wavereceiving means are provided on the same side of the paper web; andwherein either the reference ultrasonic wave receiving means comprisesone receiving element and the ultrasonic wave generating means comprisesa number of elements for generating a noise type of ultrasonic wave inthe web provided symmetrically around the receiving element, or theultrasonic wave generating means comprises one element for generating anoise type ultrasonic wave in the web and the reference ultrasonic wavereceiving means comprises a number of receiving elements providedsymmetrically around the ultrasonic wave generating element.
 2. A systemaccording to claim 1, wherein the number is even and the means havingsaid even number of elements has the elements arranged pairwise suchthat the elements in each pair have equal distances to the one elementof the other means.
 3. A system according to claim 1, wherein theultrasonic wave generating means includes said number of elements; andall said elements are provided at the side of a line through thereceiving element of the reference ultrasonic wave receiving meansdirected in the machine direction of the moving paper web.
 4. A systemaccording to claim 1, wherein the ultrasonic wave generating meansincludes at least two hard dry friction contact elements in contact withthe moving paper web for generating a noise type of ultrasonic wave inthe web, a contact dimension perpendicular to the direction of themoving paper web and a distance between the friction contact parts beingmuch less than a wavelength of the ultrasonic wave to be indicatedgenerated in the paper web; andwherein the receiving element of thereference ultrasonic wave receiving means is located in between thefriction contact elements.
 5. A system according to claim 4, wherein thefriction contact elements are made of hard alloy material and comprisetips contacting the web covered by a material absorbing ultrasonicwaves.
 6. A system according to claim 4, wherein each friction contactelement of the ultrasonic wave generating means on parts turned from thepaper web is covered by a noise shield protecting the referenceultrasonic wave receiving means from dust caused by friction betweeneach friction contact element and the web.
 7. A system according toclaim 1, wherein the pick-up ultrasonic wave receiving means is locatedabove and close to a rotating cylinder of the paper-making machineprovided under the web and is positioned, relative to a direction ofmovement of the web from the ultrasonic wave generating means towardsthe rotating cylinder, at a predetermined location downstreams from aline where the moving web first touches a roll surface of the cylinder;andfurther comprising a first noise shield located near the pick-upultrasonic wave receiving means for shielding the pick-up ultrasonicwave receiving means from airborne noise, the edge of the first shieldturned from the pick-up ultrasonic wave receiving means being located insaid direction of movement downstream from the line where the moving webfirst touches the cylinder, and the ultrasonic wave element(s) of thepick-up ultrasonic wave receiving means is (are) placed close to an edgeof the shield turned towards the pick-up ultrasonic wave receivingmeans.
 8. A system according to claim 7, further comprising a secondnoise shield located between the ultrasonic wave generating means andthe pick-up ultrasonic wave receiving means for shielding the pick-upultrasonic wave receiving means from sound and dust generated from theultrasonic wave generating means.
 9. A system according to claim 1,wherein a lateral dimension of the receiving elements of the referenceultrasonic wave receiving means are at least 10 times less than awavelength of the ultrasonic wave in the paper web, and the receivingelements of the reference ultrasonic wave receiving means are placed ata distance from the web less than a wavelength of the ultrasonic wavereradiated from the paper web.
 10. A system according to claim 1,wherein the pick-up ultrasonic wave receiving means comprises at leasttwo adjacent pick-up elements to receive contactlessly the ultrasonicwave generated in the web by the ultrasonic wave generating means andreradiated by the web; processing means to combine outputs from the atleast two pick-up receiving elements; computing means for processingoutputs from the reference ultrasonic waver receiving means and from theprocessing means, and determining a delay time between these outputs.11. A system according to claim 10, wherein a distance between theadjacent pick-up elements, in a plane parallel to the paper web, is halfof the wavelength in air at the centre frequency of a band width usedfor measurements.
 12. A system according to claim 1, wherein theultrasonic wave receiving means are placed along a straight line in amachine direction of the moving paper web, which is the directiondirected from the ultrasonic wave generating means towards the pick-upultrasonic wave receiving means, in order to obtain a time betweengeneration of the ultrasound wave part of interest to monitor andpropagating in the web and the reradiation of the same wave at pick-upelements of the pick-up ultrasonic wave receiving means in order toderive Tensile Stiffness Index in the machine direction.
 13. A systemaccording to claim 1, wherein the pick-up ultrasonic wave receivingmeans can be oriented obliquely in relation to the reference ultrasonicwave receiving means at chosen angle(s) to a machine direction of themoving paper web, which is a direction directed from the ultrasonic wavegenerating means towards the pick-up ultrasonic wave receiving means, inorder to obtain a time between generation of the ultrasound wave part ofinterest to monitor and propagating in the web and the reradiation ofthe same wave at receiving elements of the pick-up ultrasonic wavereceiving means in order to derive the Tensile Stiffness Index in anoblique direction.
 14. A system according to claim 13, wherein resultsfrom measurements in several oblique directions are combined to derivethe Tensile Stiffness Index in a cross direction of the paper machine.15. A system according to claim 10, wherein the computing meansdetermines the delay time as a zero-cross of the Hilbert transform of across-correlation function between the outputs of the pick-up ultrasonicwave receiving means and the processor, corresponding to the maximumvalue of the cross-correlation function.
 16. A system according to claim15, wherein a Hilbert window is created in the time domain and isshifted until a peak location in time of the cross-correlation functionis found and a sharp peak is derived.